I. Field of the Invention
The present invention relates to the Shannon bound on communications capacity and also relates to symbol modulation for high-data-rate wired, wireless, and optical communications and includes the symbol modulations phase-shift-keying PSK, quadrature amplitude modulation QAM, bandwidth efficient modulation BEM, gaussian minimum shift keying GMSK, pulse position modulation PPM, and the plurality of current and future modulations for single links and multiple access links which include time division multiple access TDMA, orthogonal frequency division multiple access 0FDMA, code division multiple access CDMA, spatial division multiple access SDMA, frequency hopping FH, optical wavelength division multiple access WDMA, orthogonal Wavelet division multiple access OWDMA, pulse position modulation PPM, combinations thereof, and the plurality of radar, optical, laser, spatial, temporal, sound, imaging, and media applications. Communication application examples include electrical and optical wired, mobile, point-to-point, point-to-multipoint, multipoint-to-multipoint, cellular, and satellite communication networks.
II. Description of the Related Art
The Shannon bound is the Shannon capacity theorem for the maximum data rate C and equivalently can be restated as a bound on the corresponding number of modulation bits per symbol as well as a bound on the communications efficiency and is complemented by the Shannon coding theorem. From Shannon's paper “A Mathematical Theory of Communications” Bell System Technical Journal, 27:379-423, 623-656, October 1948 and B. Vucetic and J. Yuan's book “Turbo Codes”, Kluwer Academic Publishers 2000, the Shannon capacity theorem, the corresponding Shannon bound on the information bits per symbol b=bits/symbol=bits/(Ts interval), the Shannon bound on the communications efficiency η, and the Shannon coding theorem can be written as equations (2).Shannon bounds and coding theorem1. Shannon capacity theoremC=B log2(1+S/N), bits/second=Channel capacity in bits/second for an additive white Gaussian noise AWGN channel with bandwidth B=Maximum rate at which information can be reliabily transmitted over a noisy channel where S/N is the signal-to-noise ratio in B2. Shannon bound on b and ηUsing equations (1) and the assumption that the symbol rate (1/Ts) is maximized when equal to the bandwidth B which is equivalent to the equation TsB=1, enables the equation for C to be rewritten to calculate max{b} as a function of S/N, and to calculate Eb/No as a function of the max{b} which reads the maximum value of the number of information bits per symbol b. Since the communications efficiency η=b/(TsB) in bits/sec/Hz it follows that maximum values of b and η are equal.max{b}=log2(1+S/N)=max(η)Eb/No=[2^max{b}−1]/max{b}3. Shannon coding theorem for the information bit rate Rb For Rb<C there exists codes which support reliable communicationsFor Rb>C there are no codes which support reliable communications  (2)wherein Eb is the energy per bit b, No is the noise power density. and S/N=bEb/No. Reliable communications in the statement of the Shannon coding theorem 3 means an arbitrarily low bit error rate BER.
Current communications performance is represented by the Shannon bound, QAM, and PSK performance for b vs. Eb/No and for b vs. S/N in FIGS. 1,2 respectively. FIG. 1 plots the number of information bits per symbol b versus measured Eb/No for 4-PSK, 8-PSK, 16-QAM, 64-QAM, 256-QAM, 4096-QAM for both uncoded and Turbo coding. The 4-PSK, 8-PSK are 4-phase, 8-phase phase shift keying modulations which respectively encode 2,3 bits per symbol and 16-QAM, 64-QAM, 256-QAM, 1024-QAM are 16, 64, 256, 4096 state QAM modulations which respectively encode 4, 6, 8, 12 bits. For no coding the information bits per symbol b is equal to the modulation bits per symbol bs so that b=bs=2, 3, 4, 6, 8, 12 bits per symbol respectively for 4-PSK, 8-PSK, 16-QAM, 64-QAM, 256-QAM, 4096-QAM. FIG. 2 plots b versus the measured S/N for these modulations for both uncoded and Turbo coding. Shannon bound performance is calculated using equations (2). Turbo coding performance assumes a modest 4 state recursive systematic convolutional code RSC, 1024 bit interleaver, and 4 Turbo decoding iterations. The assumed coding rates R=¾, ⅔, ¾, ⅔, ¾, ⅔ reduce the information bits per symbol to the respective values b=bs=1.5, 2, 3, 4, 6, 8 bits. Performance data is from C. Heegard and S. B. Wicker's book “Turbo Coding”, Kluwer Academic Publishers 1999, B. Vucetic and J. Yuan's book “Turbo Codes”, Kluwer Academic Publishers 2000, J. G. Proakis's book “Digital Communications”, McGraw Hill, Inc. 1995, L. Hanzo, C. H. Wong, M. S. Lee's book “Adaptive Wireless Transceivers”, John Wiley & Sons 2002, and the other listed references.
FIGS. 1 and 2 only consider the 4-PSK and 8-PSK modulations for PSK since 2-PSK is somewhat less efficient than 4-PSK, and 16-PSK is somewhat less efficient than 16-QAM. For bs=4 bits/symbol=bits/(Ts interval) and higher, only QAM is considered since it is well known to be the more efficient modulation in the sense of requiring the lowest Eb/No and S/N for given b, bs and is well known to be the only modulation capable of supporting to bs=12 bits/symbol=bits/(Ts interval) and higher.
Gaussian minimum shift keying GMSK modulation and waveform is used for the wireless cellular phone standard GSM and for space and military applications which use GSMK because it is a constant amplitude signal bandwidth efficient modulation BEM and waveform with a relatively high communications efficiency η. A constant amplitude modulation and waveform allows the power amplifier in the transmitter to operate at the saturation level with no backoff required, which is the most efficient operational mode of a power amplifier. With non-constant modulation as well as non-constant signals the input signal to the power amplifier must be backed off 2-to-10 dB in order to maintain linearity of the signal transmitted by the power amplifier. A backoff of 2-to-10 dB means the output signal is 2-to-10 dB lower than the maximum output level of the power amplifier, and this means a loss of 2-to-10 dB in the communications link compared to the transmitted signal level when the output amplifier is operating at the saturation level. This constant signal amplitude advantage of GMSK is only realized for single channel links such as the return link from the user to the hub or access point for cellular networks, and for some space and military applications. For the forward links of cellular networks which simultaneously transmit multiple channels of GMSK the composite transmitted waveform is non-constant and inherently Gaussian in character with no significant envelope advantage over other multiple channel waveforms with respect to the required power amplifier backoff.
FIGS. 3,4 are representative modulator and demodulator architectures for GMSK. In FIG. 3 the digital parameters 1 identify the bit lengths of the phase quantization, number of digital samples per pulse, and the digital-to-analog conversion DAC. Signal processing 2 parameters are the digital word size, bit duration Tb, Gaussian impulse function which is the FM frequency pulse for each symbol, and the integrated value of the impulse function which is the phase. Inputs to the GMSK FM modulator are the stream of digital words 3. Each digital word modulates a Gaussian pulse and the FM modulator integrates this train of overlapping Gaussian frequency pulses to generate the information bearing phase history. The stream of phase angle samples {ejφk(n)} 4 from the GMSK FM modulator are handed over to the inphase and quadrature digital-to-analog converters DACs and low pass filtered LPF 5, outputs are single sideband upconverted to an intermediate frequency 6 and then handed over to the IF-RF front end for transmission.
In FIG. 4 the signal processing 7 parameters for the demodulator identify the received down-converted intermediate frequency IF signal, band-pass filter BPF, inphase and quadrature detector I/Q, analog-to-digital converter ADC, the complex sample rate, complex baseband sample, receive Rx signal amplitude, and the baseband pulse amplitude modulation PAM filters which recover shifted versions of the transmitted integrated Gaussian frequency pulses. The GMSK demodulator 8 receives the IF signal from the RF-IF front end, performs bandpass filtering, recovers the inphase and quadrature baseband I/Q components which are digitized by the ADC. Digitized signals are synchronized, filtered by a bank of pulse amplitude modulation PAM filters to recover GMSK modulation responses which are weighted by the possible trellis states of the maximum likelihood path through the trellis, and the estimated transmitted digital words are then recovered by a maximum likelihood detector or by a Viterbi or maximum a-posteriori MAP type algorithm.
FIG. 5 is a representative modulation transmitter block diagram for implementation. Signal processing starts with the stream of user input data words (dk} 13 with k indexed over the words. Frame processor 14 accepts these data words and performs the error detection cyclic redundant coding CRC and Turbo error correction encoding and frame formatting, and passes the outputs to the modulator 15 which encodes the frame data words into modulated symbols that are waveform encoded by convolving with the waveform impulse response in, combination with the multiple-access channelization. Output encoded complex baseband signal {z(ti)} at the digital sample times {ti} are digital-to-analog DAC converted 16 and single sideband SSB upconverted to the real signal v(t) 17 at an intermediate frequency IF. For multiple beam antennas 18 the beam coefficients for each beam element for each complex digital sample are processed and the individual digital streams are handed off to the corresponding antenna elements where they are SSB upconverted to an IF and processed by the analog front end 19 at each element and the array of elements form the beams and within each beam the transmitted signal is similar to the real radio transmission frequency RF signal v(t) 20 at the RF carrier frequency f0 with an amplitude that is the real part of z(t) with the phase angle φ.
FIG. 6 is a representative demodulation receiver block diagram. Wavefronts 21 incident at the receiver antenna for the nu users u=1, . . . , nu≦Nc are combined by addition in the antenna to form the receive Rx signal {circumflex over (v)}(t) at the antenna output 22 where {circumflex over (v)}(t) is an estimate of the transmitted signal v(t) 20 in FIG. 6, that is received with errors in time Δt, frequency Δf, phase Δθ, and with an estimate {circumflex over (z)}(t) of the transmitted complex baseband signal z(t) 20 in FIG. 6. This received signal {circumflex over (v)}(t) is amplified and downconverted by the analog front end 23 and then synchronized (synch.) and analog-to-digital ADC converted 24. In 25 the waveform is removed to detect the data symbols in combination with the recovery of the symbol inputs to the multiple access channels. In 26 the recovered data symbols are CRC detected. Turbo decoded, and the frame removed by the frame processor 26 to recover estimates {{circumflex over (d)}k} 28 of the transmitted user data words.